Convergence of finite difference schemes for the Benjamin-Ono equation
Provides theoretical convergence guarantees for numerical schemes of a nonlinear dispersive PDE, relevant to researchers in numerical analysis and PDEs.
The paper proves convergence of fully discrete finite difference schemes for the Benjamin-Ono equation under sufficiently regular initial data, covering both decaying and periodic cases, with numerical examples illustrating the result.
In this paper, we analyze finite difference schemes for Benjamin-Ono equation, u_t = uu_x + Hu_{xx}, where H denotes the Hilbert transform. Both the decaying case on the full line and the periodic case are considered. If the initial data are sufficiently regular, fully discrete finite difference schemes shown to converge to a classical solution. Finally, the convergence is illustrated by several examples.